A linearized energy-conservative scheme for two-dimensional nonlinear Schrödinger equation with wave operator

Yuna Yang, Hongwei Li and Xu Guo

Applied Mathematics and Computation, 2021, vol. 404, issue C

Abstract: Based on the invariant energy quadratization approach, we propose a linear implicit and local energy preserving scheme for the nonlinear Schrödinger equation with wave operator, that describes the solitary waves in physics. In order to overcome the difficulty of designing an efficient scheme for the imaginary functions of the nonlinear Schrödinger equation with wave operator, we transform the original problem into its real form. By introducing some auxiliary variables, the real form of nonlinear Schrödinger equation with wave operator is reformulated into an equivalent system, which admits the modified local energy conservation law. Then the equivalent system is discretized by the finite difference method to yield a linear system at each time step, which can be efficiently solved. A numerical analysis of the proposed scheme is conducted to show its uniquely solvability and convergence. Our proposed method is validated by numerical simulations in terms of accuracy, energy conservation law and stability.

Keywords: Nonlinear Schrödinger equation with wave operator; Invariant energy quadratization; Energy preserving scheme; Stability (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300321003246
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:404:y:2021:i:c:s0096300321003246

DOI: 10.1016/j.amc.2021.126234

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().